Working Paper Protection against major catastrophes: An economic perspective

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1 econstor Der Open-Access-Publikationsserver der ZBW Leibniz-Informationszentrum Wirtschaft The Open Access Publication Server of the ZBW Leibniz Information Centre for Economics Wenzel, Lars; Wolf, André Working Paper Protection against major catastrophes: An economic perspective HWWI Research Paper, No. 137 Provided in Cooperation with: Hamburg Institute of International Economics (HWWI) Suggested Citation: Wenzel, Lars; Wolf, André (2013) : Protection against major catastrophes: An economic perspective, HWWI Research Paper, No. 137 This Version is available at: Nutzungsbedingungen: Die ZBW räumt Ihnen als Nutzerin/Nutzer das unentgeltliche, räumlich unbeschränkte und zeitlich auf die Dauer des Schutzrechts beschränkte einfache Recht ein, das ausgewählte Werk im Rahmen der unter nachzulesenden vollständigen Nutzungsbedingungen zu vervielfältigen, mit denen die Nutzerin/der Nutzer sich durch die erste Nutzung einverstanden erklärt. Terms of use: The ZBW grants you, the user, the non-exclusive right to use the selected work free of charge, territorially unrestricted and within the time limit of the term of the property rights according to the terms specified at By the first use of the selected work the user agrees and declares to comply with these terms of use. zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics

2 Protection against major catastrophes: an economic perspective Lars Wenzel, André Wolf HWWI Research Paper 137 Hamburg Institute of International Economics (HWWI) 2013 ISSN X

3 Lars Wenzel Hamburg Institute of International Economics (HWWI) Heimhuder Str Hamburg Germany Phone: +49 (0) Fax: +49 (0) André Wolf Hamburg Institute of International Economics (HWWI) Heimhuder Str Hamburg Germany Phone: +49 (0) Fax: +49 (0) HWWI Research Paper Hamburg Institute of International Economics (HWWI) Heimhuder Str Hamburg Germany Phone: +49 (0) Fax: +49 (0) ISSN X Editorial Board: Prof. Dr. Thomas Straubhaar (Chair) Prof. Dr. Michael Bräuninger Hamburg Institute of International Economics (HWWI) January 2013 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the publisher.

4 Sponsored by Protection against major catastrophes: an economic perspective Lars Wenzel & André Wolf Special thanks for excellent research support to Simon Piaszeck Hamburgisches WeltWirtschaftsInstitut (HWWI)

5 Table of contents 1 Introduction 5 2 Economy-wide effects of catastrophes Direct effects: physical destruction and losses of human life Indirect short-term effects: supply chain disruptions and recovery measures Indirect long-term effects: impact on investment decision 12 3 Coping with catastrophe risk in a decentralized economy Protective measures and pro-active response Insurance and alternative financial hedging instruments 23 4 Policies to promote private security investments 28 5 Conclusion 31 6 References 33 7 Appendix 40 Table of figures Figure 1: Stylized output response at different positions in the business cycle 11 Figure 2: Stylized long-term evolution of output according to different theories 14 Figure 3: Series and Parallel Systems, with Component Failure 18 Figure 4: Evolution of trade volumes of CAT Bonds 28 4

6 1 Introduction This paper intends to further understanding of catastrophic events by reviewing the economic literature on their effects as well as potential means of dealing with the corresponding risks and uncertainties. Since 2000, the world has seen a number of catastrophes including terrorist attacks in the United States and Europe, tsunamis in Southeast Asia and Japan as well as volcanic eruptions in Iceland. All of these have had significant impacts on human well-being and economic activity beyond the regional level. In an increasingly populous and globalized world, these types of events and their repercussions are likely to increase. Hence, it is important to ensure that government and private entities cooperate in an attempt to reduce risks of catastrophes. Generally, two types of catastrophes are distinguished: man-made and natural. Table A1 shows a list of recent natural disasters with estimated insurance damages. Manmade catastrophes can result from terrorism, crime or human error. While the nature of the damages does not differ substantially, these types of catastrophes require different counter-measures. The reason for these events' destructive potential lies in the increasing interconnectedness of modern societies and economies. This culminates in so-called critical infrastructure, which is defined by the European Commission (2004) as follows: "Critical infrastructures consist of those physical and information technology facilities, networks, services and assets which, if disrupted or destroyed, would have a serious impact on the health, safety, security or economic well-being of citizens or the effective functioning of governments in the member states. Mutual dependence can thus set of cascading effects, which can further aggravate damages. As an example, a failure of a power plant is likely to have knock-on effects on customers and potentially suppliers. The exploration of these effects and the corresponding risks is the aim of the paper. Thus, Section 2 will outline three kinds of effects resulting from catastrophic events. These are the direct, indirect short-term and indirect long-term effects. The focus will be on real, rather than monetary outcomes. In Section 3, the options available to private actors in reducing or hedging catastrophes risks are outlined. These consist of prevention and pro-active measures on the one hand and insurance or risk hedging on the other hand. Section 4 outlines the options available to governments and assesses policies aimed at addressing market failures in the security market. Finally, Section 5 will conclude this review of the existing literature. 5

7 2 Economy-wide effects of catastrophes 2.1 Direct effects: physical destruction and losses of human life As an immediate economic impact of any large-scale disaster, one has to recognize the loss of physical assets and human life occurring instantly or in the course of rescue operations. In a macroeconomic view, destruction of any form of physical capital (i.e. non-financial wealth) represents a reduction of the economy s productive capacity. In evaluating the adverse consequences of such a productivity shock, the value of all resource destroyed needs to be expressed in terms of a single monetary measure. With respect to privately owned assets, observed market prices are principally suitable for this task, provided that they sufficiently reflect future revenue flows resulting from a productive usage. 1 Assessing the value of public infrastructure can be much more challenging, especially when it displays features of pure public goods (like motorways, bridges). These goods are provided either free of charge or at highly regulated prices. Hence, it is largely impossible to make statements on losses based on the costs of use. For this reason, indirect methods measuring the extent of business interruptions caused by the infrastructure breakdown are often made use of (Rose, 2004). In case of transport infrastructure, loss estimates should both account for the inability to make shipments and the travel time value of commuters (Gordon et al., 1998). Even more challenging is an economic assessment of the loss of a human life. A common approach is to draw an analogy to physical assets and estimate the future flow of foregone lifetime earnings (Rice et al., 1967). For instance, in an examination of the costs of the September 11 attacks in New York 2001, Bram et al. (2002) calculate the loss of total earnings of all victims killed by adding up their current annual incomes from 2001 onwards to the year they would have retired. The resulting sum of 7.8 billion USD is considered a proxy for the loss of human capital. This was simply added to the loss of physical capital (21.6 billion USD) to arrive at a measure of 29.4 billion USD for the entire loss. Empirical evidence on damage determinants Concerning the determinants of this direct damage, a strand of empirical literature tries to identify linkages to the level of macroeconomic development. One central observation is that developing countries tend to incur bigger monetary damages from catastrophes relative to their GDP than developed countries (Rasmussen, 2004; Loayza 1 See Rose (2004) for a discussion of this issue. 6

8 et al., 2012). However, significance and direction of a potential causal effect are a priori unclear. For this reason, researchers started to regress meaningful damage measures (typically either number of deaths or monetary damage as a share of GDP 2 ) on a range of macroeconomic indicators. Since both economic development and vulnerability towards large-scale threats are linked to geography 3, heterogeneity between countries needs to be controlled for, commonly by means of a Panel Data model. In this vein, Burton et al. (1993) were the first to detect a modestly negative impact of GDP per capita on the death toll from natural disasters, suggesting indeed a linkage to economic development. An obvious explanation would be that richer countries can afford to delegate more resources both to protective measures and to subsequent rescue operations. This result is confirmed by later works such as Kahn (2005) and Toya & Skidmore (2007). Raschky (2008) seeks to test whether this relationship is linear or not. He finds evidence for nonlinearity in the form that the effect diminishes with increasing level of GDP, implying that economic progress cannot reduce damages indefinitely. Further attention has been devoted to a potential role of institutions. Kahn (2005) finds a negative impact of a nation s level of democracy on the number of deaths associated with a disaster, even when controlling for GDP. The author argues that the presence of democratic institutions lowers the overall level of corruption in the economy, thus preventing the misuse of resources designated to be invested in protective measures. Similarly, Raschky (2008) detects evidence for a similar influence of both government stability and investment climate. These factors might also be interpreted as proxies for the efficiency of damage prevention and mitigation. Skidmore & Toya (2007) go one step further by even integrating educational attainment (measured in average years of schooling) as an additional explanatory variable into damage estimation. Higher educational attainment is also shown to reduce average losses, possibly because the knowledge gain allows individuals to make more wise decisions on prevention. Finally, Anbarci et al. (2005) shed light on the impact of distributional concerns on damage exposure. They show that not only a country s total level of income, but also the degree of economic inequality matters. Among similarly developed countries, those that exhibit a lower degree of inequality 4 also exhibit a lower average level of fatalities from earthquakes. This is attributed to the role of inequality for incentives to undertake collective action, especially in developing countries. As Freeman et al. (2003) 2 In most studies, data is taken from the OFDA/CRED International Disaster Database collected by the Center for Research on the Epidemiology of Disasters (CRED) in Brussels. 3 For instance, Heger et al. (2008) point out that small islands are especially vulnerable, given their strong dependence on the sensitive sectors agriculture and tourism. 4 The inequality measure applied by Anbaci et al. (2005) is the Gini coefficient for the ownership distribution of agricultural land. 7

9 note for the situation of least developed countries, it s typically the poorest individuals which are the most vulnerable, as they cannot afford the higher prices of land in less disaster-prone areas. On the other hand, the richest individuals have low incentives to contribute to collective protection, given their lower exposure and their higher capability to protect themselves. Very unequal societies thus tend to be unable to come to a satisfying agreement on collective spending, which implies a high degree of vulnerability for a significant part of the population. 2.2 Indirect short-term effects: supply chain disruptions and recovery measures The economic loss associated with physical destruction alone can be devastating enough, but economists have also drawn attention to the less visible costs of catastrophes. Most importantly, indirect costs can result from a temporary drop in the productive capacities of firms in disaster-struck areas. In the wake of a large-scale disaster, production can be subject to capacity declines for several reasons: damage done to buildings and machinery, impassability of transport routes, the priority of rescue operations or simply failure of communication and general confusion. This can not only impair the profits of firms facing these capacity constraints, but also the profits of their commercial partners. Interruptions in the supply of intermediate goods to downstream producers will force them to change their production schedules as well. If this concerns essential inputs, it might even render them unable to fulfill their own sales contracts. In addition, if a capacity decline initiates a cutback in production, it could lower the demand for intermediate inputs by affected firms. Hence, upstream producers might also experience a decrease in sales. Given that these upstream producers are again buyers of some external inputs, the shock is still further transmitted to their suppliers. In this way, a supply shock initially focused on just a subset of sectors can spill over to other sectors along the supply chain and eventually harm the whole economy via the channel of external input requirements. These second-order effects are especially pronounced when they involve the interruption of lifeline services such as electricity and gas, which disturb business operations in all sectors simultaneously. Business surveys such as Tierney (1995) and Dahlhamer & Tierney (1998) indicate that disaster-induced business closures can to a much larger extent be traced back to indirect effects like lifeline outages than to immediate physical damage. Precisely, Alesch et al. (1993) and Tierney (1995) find that small firms are particularly vulnerable to supply chain disruptions, possibly due to their heavier dependence on external inputs. 8

10 Analyzing the extent of business interruptions: Input-Output Analysis To analyze the vulnerability of the aggregate economy, Input-Output Analysis and its extensions represent the methodology most favored by both economists and engineers (Haimes & Jiang, 2001; Rose & Liao, 2005; Hallegatte, 2008). By modeling the whole set of input-output relations between sectors as one system of linear equations, estimates of the impact of any (real or counterfactual) disaster-driven shock on sector production can be derived. Since these estimates are based on equilibrium outcomes, they account for the whole complexity of contagion effects. Therefore, they can offer additional insights compared to alternative strategies like econometric analysis, which primarily rest on ex-post comparisons of the economies aggregates before and after the occurrence of a catastrophe. Moreover, Input-Output Analysis allows researchers to extend the geographical dimension of damage estimation. Neighboring regions of a disaster-struck area, while physically unaffected, might still experience an economic slowdown due to trade-based linkages. Price increases resulting from adverse supply shocks propagate via exports to consumers in other areas, lowering their real income as well. 5 Another factor contributing to the dissemination of this method is its relative ease of application. In the most basic setting, parameter calibration only requires national account information. The downside of this, however, is the restrictiveness. With respect to disaster research, the most serious shortcoming in this regard is the lack of behavioral flexibility: input shares are assumed to remain fixed; consumer demand is treated as exogenous 6. As a consequence, estimated damages based on the standard Input- Output method can potentially exhibit a considerable upward bias, as they do not reflect the natural resilience of the economy. Accounting for channels of damage mitigation Following Rose (2004), we define economic resilience as the set of all responses to catastrophes that limit the damage done or fasten the economy s recovery. 7 These responses can take place at different levels, including single individuals, households, firms, governments and even institutions (like changes in the price formation on markets). In this, a key factor is the substitutability of goods. As a response to temporary shortages of certain commodities and services, consumers could switch to substitutes, thereby relieving market pressure. Firms could try to compensate the breakdown of some machinery by increasing the workload of their employees. Other forms of resili- 5 In estimating losses from a range of worldwide disasters by means of a CGE model, Sahin (2011) shows that accounting for these rippling effects produces significantly larger estimates of total damages than by just considering the sum of individual country losses. 6 For a detailed discussion of the Pros and Cons of using Input-Output-Analysis in damage estimation, see Kowalewski (2009). 7 Note that other authors like Bruneau et al. (2003) also include ex-ante prevention measures in the definition of resilience. 9

11 ence include the use of inventories or a switch to self-produced inputs (e.g. the use of backup generators in case of electricity disruption) (Rose et al., 2005). Opportunities like these can be integrated into damage assessment in a variety of ways. For instance, a range of attempts have been made to adjust standard Input- Output Analysis to accommodate features of resilience (Duchin, 2009; Henriet & Hallegatte, 2008; Oliva et al., 2010). A more natural approach is to resort to Computable General Equilibrium (CGE) modeling, where market outcomes are truly microfounded, i.e. are derived from optimizing behavior at the individual level. However, the increase in flexibility associated with the modeling of preferences also raises the data requirements for parameter calibration. In addition, parameter specification is complicated by the fact that the degree of input substitutability is highly sensitive to the length of the examined response period. In the very short-run, firms are still dependent on existing contracts, substitutability can thus presumed to be very low. For this scenario, Input-Output Analysis (or alternatively a CGE model with a very low elasticity of input substitution) can yield adequate estimates. For a medium-run analysis, a higher level of substitutability should be presumed, asking for the flexibility of a CGE or similar approach (Rose & Guha, 2004). Concerning the lengths of these distinct recovery phases, no general statements can be made, as they again depend on nature and extent of the analyzed event. Consequently, existing results are highly specific to the chosen settings. A further obstacle in parameter choice is the tendency of people to show different behavioral patterns in crisis situations, e.g. being forced to cope with scarcities could render them more inventive. 8 In this vein, Rose (2004) further distinguishes between inherent and adaptive resilience, the latter reflecting extra-efforts of people to compensate supply chain disruptions. Moreover, the functioning of markets as coordination devices might be generally disturbed due to the vast extent of insecurity and information gaps large-scale disasters bring about. A consequence is that observations made in pre-disaster situations often do not represent valid indicators for actual crisis behavior. The impact of reconstruction activities Another factor aside from resilience that can damp output losses in the medium-run is the demand surge associated with reconstruction. Naturally, this mostly favors the sectors construction and transport 9. By raising income and thus purchasing power of workers, this could turn into a general stimulus for a post-disaster economy. The quantitative impact on total production is however conditional on the current position with- 8 For example, as documented by Rodriguez et al.(2006) for the aftermath of Hurricane Katrina. 9 See Kirchberger (2012) for evidence on the labor market effects in these sectors. 10

12 in the business cycle, as demonstrated by Hallegatte & Ghil (2008). If the disaster hits the economy in a boom phase where productive capacities are almost fully exhausted, there are no idle resources left that reconstruction could draw upon. Hence, there is no opportunity for output to increase in the reconstruction stage. Factors employed in reconstruction are then simply redirected from other activities. This can be different in recession, where capacities are usually underutilized. By making use of these additional capacities, reconstruction could indeed induce output to rise in response to a disaster. Both (idealized) situations are depicted in Figure 1. However, even if production should experience a boost due to reconstruction, this should not be misinterpreted as a positive welfare effect. Reconstruction activity merely represents the restoration of a destroyed share of the society s stock of wealth. Hence, for the purpose of welfare evaluation, reconstruction should be left aside (Rose, 2004). Figure 1: Stylized output response at different positions in the business cycle Source: Own representation To summarize, attempts to consider the impact of catastrophes on market transactions have so far brought a considerable amount of indirect effects to light. Nevertheless, barriers to a quantitative assessment of important aspects have yet prevented the establishment of a reliable net measure summarizing the multitude of these side effects. Since the relevance of supply chain effects is undisputed, enhancing the flexibility of estimation methods in that sense will continue to represent a main strand of future investigations. 11

13 2.3 Indirect long-term effects: impact on investment decision Even after reconstruction has been completed, a catastrophe can continue to affect market transactions in the economy via its influence on investment spending. This could be triggered both by changes in the current returns to certain assets and by changes in expectations. Whether this can guide the economy to a different growth path is determined by the interplay of technology and factor accumulation. Competing theories on the question of long-term damage From a neoclassical point of view, the consequences of a disaster for growth of GDP per capita are expected to be of short-term nature, i.e. should taper off over time. In aggregate terms, the direction of the short-term effect depends on the disaster s instant impact on the capital-to-labor ratio (Loayza et al., 2012). For the following discussion, we restrict our attention to catastrophes where economy-wide damage is limited to the destruction of physical assets, presuming that neither size nor future growth of the working population are affected (i.e. the impact of deaths or outmigration on total labor supply is assumed to be negligible). Hence, the formal interpretation is that of an unexpected depreciation of the economy s stock of physical capital. With shrinking marginal productivity as assumed by the standard Solow framework (Solow, 1956), the immediate impact of such a decline in physical capital is an increase in the marginal productivity of each additional amount of money saved and invested. Despite the destruction taken place, growth rates are thus expected to rise immediately after a disaster hits the economy 10. This increase, however, is not persistent, but simply serves to compensate the initial negative level effect on production. Growth slows down again such that, in the longer term, the economy approaches again the pre-disaster growth rate. As a result, production converges to its potential level in the absence of the shock, implying that disasters exert no long-run impact on an economy s productive capacities (see graph 2.A). A key assumption for this to hold is that the technology of capital usage is exogenous, i.e. remains unaffected by the cataclysmic event. This can be questioned with regards to simultaneous side effects. One effect discussed by the literature is the occurrence of a capital upgrade in the course of reconstruction. Private as well as public decision-makers might see a chance to replace destroyed assets by updated capital embodying new technologies (Albala-Bertrand, 1993). In this way, disasters could become physical equivalents to the processes of creative destruction, described as the main driving forces of technological change by Schumpeter (1934). If this takes the form of a 10 When considering endogenous savings as in the Ramsey-Cass-Koopmans version (Cass, 1965), this catch-up effect is even more pronounced due to an increase of the savings quota. 12

14 one-off effect, it will not generate persistently higher growth. Nevertheless, it can induce a persistent level effect, raising the productive capacity at any future point in time (see graph 2.B). If disasters are able to stimulate innovative activity, e.g. by emphasizing the need of continuous technology upgrading as a response to disaster risk, they could even exert a positive long-run effect on the growth of GDP. Additionally, a connection between disasters and long-run growth can arise from side effects on human capital investments. The nature of this side effect is however not obvious. Depending on the type of investment rationale assumed, theoretical reasoning is able to provide arguments for both a positive and a negative impact of catastrophes on educational activities. Under the assumption of a shrinking marginal productivity for all factors, a disaster mainly characterized by the destruction of physical capital lowers the return to human capital investment relative to physical capital. A conclusion would be that people devote less of their savings to finance learning activities and more to investments into physical assets in the aftermath of a disaster. This is amplified when a catastrophe involves the destruction of educational infrastructure. If reconstruction is not undertaken soon enough, the lack of opportunities can cause a permanent setback in human capital formation, potentially guiding the economy to a lower growth path (Lucas, 1988) (see graph 2.C). Ambiguity in the direction of the effect is introduced by considering the individual trade-off between time spent working and time spent studying. As Baez et al. (2010) note, the opportunity costs of education could both rise and fall in response to a disaster. On the one hand, the necessity to engage in reconstruction activities might leave people less time for studying. On the other hand, if massive destruction leads to a cutback of labor demand and a corresponding decline of wages, perceived opportunity costs of education could also be lowered. However, the presence of an income effect on labor supply implies that even with falling wages the share of time devoted to working might be raised. This is particularly relevant in case of highly imperfect credit markets: In the presence of binding borrowing constraints, shrinking wages force workers to increase their workload in order to smooth consumption over time. This can be especially detrimental in developing countries, where children are expected to contribute to the generation of family income. Parents might be inclined to take their children out of secondary school or at least reduce family expenditures for education (Jacoby & Skoufias, 1997). The existing evidence overwhelmingly points to a negative relationship between the frequency of catastrophes and human capital formation. For instance, among the most recent investigations, cross-country studies like Cuaresma (2010) and McDermott (2012) discover a significantly negative impact on secondary school enrollment, while Kim (2008) detects a likewise negative effect on the rates of secondary school completion. An exception is Sacerdote (2008), who analyzes the effect of involuntary school 13

15 switches after Hurricane Katrina. He finds that the performance of evacuees from the lowest performing schools has considerably increased three years after displacement. This further stresses that disasters can have subtle consequences at the individual level, which in turn might also affect the economy s aggregates over a longer time horizon. Figure 2: Stylized long-term evolution of output according to different theories Log GDP 2.A: Neoclassical case Log GDP 2.B: Capital upgrading capital upgrade disaster time disaster time Log GDP 2.C: Decrease in human capital investments Log GDP 2.D: Poverty trap threshold disaster time disaster I disaster II time Source: Own representation Finally, a long-run effect on output would also be consistent with the notion of discontinuities in development. According to some theorists like Nelson (1956) and Durlauf (1991), the process of economic development is characterized by a discrete transition between distinct stages. If a threshold in the level of some critical performance measure like output or human capital is exceeded, the economy switches instantly to a superior technology (i.e. it experiences a take-off ). Within this framework, the occurrence of a major catastrophe has exactly the opposite effect. It can imply that 14

16 the economy bounces back to a lower development stage 11. In this light, Hallegatte et al. (2007) argue that economies frequently hit by disasters can end up caught in a poverty trap with persistently low growth rates. If the period between two disasters is too short for the economy to fully recover, resources desperately needed for technology adoption could be permanently stuck in reconstruction activities. This scenario is depicted in graph 2.D and seems particularly appropriate for some small developing economies. Empirical evidence on long-run effects In testing the net effect on long-term growth, a range of very different econometric strategies have been applied by researchers. A basic distinction concerns the composition of the control group in assessing the causal effect of disasters. In approaches where estimates are gained from cross-country Panel models, like Loayza et al. (2012) and Jaramillo (2009), this control group basically consists of all unaffected countries irrespective of whether they share comparable economic characteristics or not. As Cavallo et al. (2010) note, this can bias inference, as estimates might capture deviations in time trends which have nothing to do with the occurrence of the disaster. Alternative approaches therefore explicitly compare the evolution of output in disaster-struck regions with a counterfactual benchmark. This benchmark can consist of time series projections of models fitted to pre-disaster data for the country itself (Berlemann & Vogt, 2007; Hochrainer, 2009) or for a synthetic control country (Cavallo et al., 2011). This diversity of methods results in a similar diversity of outcomes. While Hochrainer (2009) and Raddatz (2009) find evidence for a negative effect of disasters on growth, the results of Jaramillo (2009) and Cavallo et al. (2010) rather suggest neoclassical long-run neutrality. Finally, Skidmore & Toya (2002) and Yasuyuki et al. (2011) even obtain positive long-run effects, which Skidmore & Toya (2002) interpret as some confirmation for the capital upgrading hypothesis. Obviously, besides the particularities of affected regions, it is also the heterogeneity of catastrophes themselves that impedes the establishment of general propositions through empirics. For instance, studies based on a categorization of disasters generally conclude that only moderate disasters can be beneficial for growth, while severe ones cannot. Moreover, developing economies are suffering from significantly worse effects, especially when they can already look back at a history of similar events (Loayza et al., 2012; Fomby et al., 2009; Jaramillo, 2009). These results point to the relevance of discontinuities like poverty traps in assessing disaster outcomes. Moreover, the analysis of Fomby et al. (2009) demonstrates the distinctiveness of specific types of catastrophes: 11 Alternatively, the same mechanism can be explained by discontinuous savings rates through subsistence consumption (see Kraay & Raddatz, (2007)). 15

17 while floods have the tendency to exert a positive impact, storms tend to have a negative one. Future approaches will thus have to devote more efforts to differentiation in order to add robust insights to this complex topic. 3 Coping with catastrophe risk in a decentralized economy 3.1 Protective measures and pro-active response In practice, decision-makers face considerable resource limitations in securing the provision of key infrastructure services. Protecting critical infrastructure against a multitude of existing threats involves various types of trade-offs. One has to decide on which type of threat to shield against, which facility to protect the most and which share of worker time to devote to security routines. Essentially, security planning can be viewed as a collection of interrelated problems of constrained optimization. While decisions can be principally based on calculus, a solution algorithm should also account for the behavioral implications. Any measure undertaken can have repercussions on the behavior of other planners as well as potential perpetrators, which in turn influence its effectiveness. In this regard, economic concepts like game theory can sharpen the senses on the strategic nature of infrastructure protection and provide the necessary intuition to deal with real-life threats. The case of independent sites This becomes already clear by considering the simplest setup of a security investment problem: the decision how to allocate a fixed budget for protective measures among a range of independent infrastructure sites, each basically exposed to the same threat. The probability that a site turns inoperative due to an attack (i.e. the failure risk) is a decreasing function of the amount of resources spent on its protection. Golany et al. (2009) have investigated optimal allocation rules for this scenario under the reasonable assumption that the defender seeks to minimize expected damage. In particular, they demonstrate how optimal spending differs between the two major types of risks: natural disasters and terrorist attacks. To minimize damage inflicted by a natural disaster, priority has to be given to the protection of those sites where the efficiency of protective measures is the highest (i.e. where the means invested can cause the strongest decline in failure risk). In contrast, when facing a terrorist threat, the most vulnerable sites (i.e. with the highest failure risk) should always be shielded with priority, even if marginal efficien- 16

18 cy of the money invested might be higher at other sides. Expected damage is minimized when all sites end up with the same degree of risk exposure. The difference is the strategic response of attackers. Provided that terrorists are not completely unaware of the strength of protection granted to different sites, they will always focus on attacking the site with the highest fatality risk after considering protection. Powell (2009) confirms these results for the scenario of a sequential game, proving that such a minmax-behavior represents a dominant strategy for a defender. Golany et al. (2009) refer to this type of risk as strategic risk, as opposed to the pure probabilistic risk associated with natural disasters. According to Brown et al. (2006), strategic risk in general represents a tougher challenge to the defender, as a rational attacker usually benefits from two prime advantages. First, she can focus on attacking a subset of very vulnerable sites, while the defender bears the responsibility to protect the complete set. Second, information on the resilience of certain targets is often public. At the same time, the defender tends to have only very limited knowledge on resources and strategic objectives of the attacker. The case of interdependent sites: insights from reliability analysis While the simple problem of defending independent sites sheds some light on the rationale of safety measures, it offers only limited guidance on the protection of realworld infrastructure. Foremost, any modeling framework should account for the strategic implications of existing interdependencies. Indeed, one distinctive feature of modern infrastructure facilities is their interconnectedness (Macaulay, 2009). Depending on the way components of a system of infrastructure services are nested, the corruption of just one component due to a catastrophic event could have severe consequences for the operability of the total system. This sensitivity to the mode of nesting, in turn, requires the use of engineering methods to determine appropriate security responses. In recent years, reliability analysis as one important interdisciplinary field in safety engineering has increasingly been applied to analyze the optimal degree of protection against external threats (e.g. Levitin, 2002; Bier et al., 2005; Azaiez & Bier, 2007). In these works, the probability of system failure is represented as a technologydependent function of failure probabilities of the single components. This is typically combined with an optimization approach: failure risk is minimized by allocating resources to the protection of single components. One fundamental concept in this kind of analysis is the distinction between series and parallel systems. It indicates in how far the functionality of the aggregate system depends on the functionality of the single components. In a pure parallel system, components are perfectly substitutable in the sense that the occurrence of system failure would require that each component gets corrupted. For instance, this can apply to systems where components are designed to carry out very similar tasks. Intuitively, the redundancy implied by this feature is advantageous to a defender. Unlike in the case of 17

19 independent facilities, the exposure to malicious attacks does not require a strict focus on the weakest components. Hence, measures to shield against both major types of risk can be undertaken in light of efficiency considerations, employing funds where they yield the biggest reduction in component risk. Figure 3: Series and parallel systems, with component failure (lower graph) Source: Own representation In a series system, the failure of just one component induces the whole system to collapse, regardless of the performance of other components. 12 This property has crucial consequences for the efficiency of investments in risk-management. Specifically, it implies that the effectiveness of a security upgrade of one component strongly hinges upon the reliability of other components. In the extreme case where one out of many components could never stand any disastrous event, investments in other components would be completely useless. Since marginal investment efficiency increases with re- 12 In cases where failure risk at component level is distributed independently, the probability that a system does not fail (i.e. that it succeeds) within a certain time span is thus simply calculated as the product of success rates of the single components. 18

20 duced vulnerability of other components, equalizing marginal efficiencies represents an optimal rule for tackling probabilistic risk. 13 However, unlike for parallel systems, this rule cannot be applied to strategic risk. A terrorist group seeking to maximize the probability of system failure by launching an attack on one of its components will always choose the most vulnerable one as their target. Hence, marginal cost efficiency is not a relevant criterion in protecting a series system against a terrorist threat. Even if investment in the stability of less vulnerable components might yield a stronger decline in component risk, it cannot improve the reliability of the aggregate system. An appropriate allocation rule is thus to shield the most vulnerable components with priority until their exposure equals the exposure of the second most vulnerable, after which an equal amount is invested into both components and so forth (Bier et al., 2005). If sufficient resources are available for risk mitigation, the optimum is characterized by a situation in which expected failure risk is equalized between all components. Hausken (2008) notes that series and parallel systems also differ substantially in the strategic position of the defender: In a pure parallel system, the defender benefits from the substitutability of components. In a pure series system, it is instead the attacker that benefits from a substitution effect: the opportunity to disable the system by attacking principally any of its single components allows her to focus her efforts on the weakest component. Complexity is added when considering alternative objective functions for the attacker (e.g. maximizing the probability of inflicting a certain level of damage on a system (Holmgren et al., 2007)) or introducing alternative defense tactics for the defender (such as deploying false targets (Hausken & Levitin, 2009). Besides, a considerable body of Operational Research literature extends the simplified dichotomy of parallel and serial systems to the more realistic case of multi-state systems consisting of series and parallel subsystems. (e.g. Levitin, 2007; Azaiez & Bier, 2007). In these setups, the defender is not only asked to decide on the optimal level of protection for the single components, but also on their optimal degree of separation. Here, separation means the extent to which the system is split into independently functioning parallel subsystems. As a consequence, results become highly sensitive to the specific type of system considered, preventing any general propositions on optimal strategies. What remains to hold is that a higher degree of redundancy in the functionality of different components (i.e. a structure more strongly based on parallel components) implies a higher overall reliability due to higher flexibility offered to the defender (Bier, 2005). 13 The exact distribution of resources resulting from an application of this rule is technology dependent. 19

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